Probability and Conditional Probability Flashcards

A box holds 9 cards numbered 1–9. A card is drawn at random. What is the probability the number is a perfect square?

Answer: 1/3

Perfect squares in 1–9 are 1, 4, 9 — that's 3 out of 9, which equals 1/3.

The two-way table below shows 200 employees categorized by department and remote-work status. Remote In-Office Engineering 40 60 Marketing 30 70 If one employee is chosen at random, what is the probability they are in Engineering and work remotely?

Answer: 1/5

40 out of 200 employees are Engineering and Remote: 40/200 = 1/5.

A bag contains 3 white balls and 7 black balls. Two balls are drawn without replacement. What is the probability both are black?

Answer: 7/15

P = (7/10)(6/9) = 42/90 = 7/15.

In a survey of 400 people, 160 prefer tea, 200 prefer coffee, and 40 prefer neither. What is the probability that a randomly selected person prefers tea, given they have a preference (i.e., they don't prefer neither)?

Answer: 2/5

Those with a preference: 400 − 40 = 360; P(tea | preference) = 160/360 = 4/9.

Events X and Y are independent. P(X) = 0.5 and P(Y) = 0.6. What is P(X and Y)?

Answer: 0.30

For independent events, P(X and Y) = P(X) × P(Y) = 0.5 × 0.6 = 0.30.

A class has 12 students: 5 freshmen, 4 sophomores, and 3 juniors. One student is selected at random. What is the probability the student is NOT a junior?

Answer: 3/4

P(not junior) = (12 − 3)/12 = 9/12 = 3/4.

A two-way table records 500 patients by treatment type and recovery outcome. Recovered Did Not Recover Treatment A 150 50 Treatment B 200 100 If a recovered patient is selected at random, what is the probability they received Treatment A?

Answer: 3/7

Total recovered = 150 + 200 = 350; P(A | recovered) = 150/350 = 3/7.